Bowing to intense pressure, House Republicans on Thursday agreed to extend the payroll-tax cut for two months. The Senate promptly signed off on the deal, ending a bitter stalemate that had threatened to hike the amount withheld from the paychecks of 160 million workers starting Jan. 1 (someone with a $50,000 annual income, for instance, would have had an extra $1,000 docked from his salary over the course of 2012). Congress can now resume work on extending the break past the two-month grace period. House Speaker John Boehner and his caucus had been insisting on a full-year cut, saying the "uncertainty" of a short-term extension would hurt businesses. So why did Republicans cave? Here, three theories:

1. They realized the public was mad... at themVulnerable House Republicans, worried about next year's reelection battle, were the ones who begged "the Republican leadership to relent," says Greg Sargent at The Washington Post. Their constituents were angry that the stalemate was threatening to take a chunk out of their paychecks — $40 a week for the average taxpayer. That's pretty solid confirmation that "the public is concluding that Republicans are the ones to blame for allowing the tax hike (to) creep ever closer to reality."

2. Obama forced GOP leaders to capitulateBoehner said digging in against the temporary extension "may not have been the smartest thing in the world." That's an understatement, says Allahpundit at Hot Air. House Republicans spoonfed President Obama the opportunity to hold "a presser to demand action with middle-class taxpayers lovingly arrayed behind him," and those Republicans "caved" just a few hours later. "Now it looks like even more of a capitulation than it is. Merry Christmas from the GOP, champ." Oh, well. At least now "our dumb national nightmare is over."

3. Boehner managed to win a (minor) concessionThis isn't the "best-possible version" of the bill hoped for, says Daniel Foster at National Review. Such a version would have fast-tracked a decision on the Keystone XL oil pipeline, included modest entitlement reform, and paid for it all without punishing new taxes. But in exchange for their cooperation, House Republicans did win "a 'technical correction' designed to 'minimize difficulties businesses might experience implementing the short-term, two-month tax cut extension.'" If this fix "really does make life easier for payroll processors, that's good!"